Question

Find the GCF of the terms and then factor. 3z(2z+9)+6(2z+9)^2

Answer 1

To factor the expression \( 3z(2z+9) + 6(2z+9)^2 \), we first identify the greatest common factor (GCF) of the two terms.

1. The first term is \( 3z(2z + 9) \).
2. The second term is \( 6(2z + 9)^2 \).

The common factor in both terms is \( (2z + 9) \).

Now, let's express each term in terms of this common factor:
- The first term, \( 3z(2z + 9) \), can be rewritten as \( (2z + 9)(3z) \).
- The second term, \( 6(2z + 9)^2 \), can be rewritten as \( (2z + 9)(6(2z + 9)) \).

Now we can factor out \( (2z + 9) \):
\[
3z(2z + 9) + 6(2z + 9)^2 = (2z + 9)(3z + 6(2z + 9))
\]

Now, simplify the expression inside the parentheses:
\[
3z + 6(2z + 9) = 3z + 12z + 54 = 15z + 54
\]

Thus, we can rewrite the factored expression as:
\[
(2z + 9)(15z + 54)
\]

Finally, we can factor out a common factor from \( 15z + 54 \). The GCF of \( 15 \) and \( 54 \) is \( 3 \):
\[
15z + 54 = 3(5z + 18)
\]

Putting it all together, we have the final completely factored form:
\[
3(2z + 9)(5z + 18)
\]

So, the fully factored expression is \( \boxed{3(2z + 9)(5z + 18)} \).